Here's a long running little gem of a Thai restaurant: Lemon Tree on Huay Kaew road near Central Department store. It's fairly small, being a typical shop-house with tables set up both on the ground floor as well as upstairs. It's airconditioned and everything is painted very bright yellow. The menu is big and very varied, there are some wonderful dishes there to try out. Prices are moderate, most dishes cost around 60 baht.
Lemon Tree actually have a secon branch that's very well hidden inside the International Center building of Chiang Mai University. (Not inside CMU but in pretty much the last soi of Nimmanhaemin Road on the left, so closest to Suthep Road. This is the soi that gets closed half way down at nighttime.) Still the Huay Kaew branch is probably the better choice, it just feels a bit brighter and more popular. Service is good and very fast.
It's on Huay Kaew road, close to Central but on the opposite side of the road, close to the U-turn in front of the Shell gas station. Parking a car can be a bit of an issue there, either park in the soi where the Suki restaurant is, or park at the "12 Huay Kaew" (Sipsong Huay Kaew) entertainment mall. Parking there is not free, but with the parking ticket you can get the full amount deducted from your bill at Lemon Tree.